1-10 11-20 21-30 31-40 41-50 51+ 8 7 6 5 4 3 2 1 Histograms © T Madas

How do we present Continuous Data? Continuous Data can only be presented in groups We can only present Grouped Continuous Data The main graph for Grouped Continuous Data is: A Histogram © T Madas

Response Times to a Maths Question f 14 12 10 8 6 4 2 Class interval (seconds) Frequency f 0 ≤ t < 10 12 10 ≤ t < 20 14 20 ≤ t < 30 7 30 ≤ t < 40 8 40 ≤ t < 50 5 t 50 ≤ t < 60 4 0 10 20 30 40 50 60 © T Madas

Response Times to a Maths Question f 0 10 20 30 40 50 60 14 12 10 8 6 4 2 A histogram looks like a bar chart but: Continuous Data means NO GAPS between bars Histogram © T Madas

This seems a small difference between a bar chart and a Histogram. Is that it? NO © T Madas

The real difference between Bar Charts and Histograms is: In a Bar Chart the lengths of the bars are proportional to the frequency they represent. In a Histogram the areas of the rectangles are proportional to the frequency they represent. © T Madas

Response Times to a Maths Question f 0 10 20 30 40 50 60 14 12 10 8 6 4 2 The heights of the bars represent frequency only if the groups are of equal intervals © T Madas

unequal width intervals Histograms with unequal width intervals © T Madas

Reaction Times in a Chemistry Experiment Class interval (seconds) ? Frequency Density Frequency f 0 ≤ t < 4 3 0.75 Frequency density 4 ≤ t < 5 8 8 5 ≤ t < 6 9 9 Frequency Density Frequency = 6 ≤ t < 7 13 13 Class width 7 ≤ t < 8 5 5 t 8 ≤ t < 10 6 3 0 1 2 3 4 5 6 7 8 9 10 © T Madas

Reaction Times in a Chemistry Experiment Class interval (seconds) 14 12 10 8 6 4 2 Frequency Density Frequency f 0 ≤ t < 4 3 0.75 Frequency density 4 ≤ t < 5 8 8 5 ≤ t < 6 9 9 6 ≤ t < 7 13 13 7 ≤ t < 8 5 5 t 8 ≤ t < 10 6 3 0 1 2 3 4 5 6 7 8 9 10 © T Madas

Another Example © T Madas

Lengths of a certain Plant’s Leaves Class interval (cm) ? Frequency Density Frequency f 0≤L<4 8 2 Frequency density 4≤L<6 10 5 6≤L<8 12 6 Frequency Density Frequency = 8≤L<9 13 13 Class width 9≤L<11 14 7 L 11≤L<15 6 1.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 © T Madas

Lengths of a certain Plant’s Leaves Class interval (cm) 14 12 10 8 6 4 2 Frequency Density Frequency f 0≤L<4 8 2 Frequency density 4≤L<6 10 5 6≤L<8 12 6 8≤L<9 13 13 9≤L<11 14 7 L 11≤L<15 6 1.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 © T Madas

Exam Question © T Madas

The area of the rectangles of a histogram represent frequency The histogram below gives information about the times 120 pupils spent on their last Maths homework. Use the histogram to complete the frequency table. 5 4 3 2 1 Time (t min) Frequency 0 < t ≤ 10 20 The area of the rectangles of a histogram represent frequency 10 < t ≤ 15 25 Frequency density 15 < t ≤ 30 45 30 < t ≤ 60 30 10 20 30 40 50 60 Time, in minutes © T Madas

Exam Question © T Madas

Complete the histogram and the frequency table. The histogram and the table below gives information about the weights of 120 pupils in Year 11 Complete the histogram and the frequency table. 5 4 3 2 1 The area of the rectangles of a histogram represents frequency Weight (w kg) Frequency 30 < w ≤ 40 10 40 < w ≤ 55 45 Frequency density 55 < w ≤ 60 20 60 < w ≤ 90 45 30 40 50 60 70 80 90 Weight, in kg © T Madas

© T Madas

The area of the rectangles of a histogram represents frequency The histogram below shows the age distribution of accident and emergency admissions in the Colby City Hospital for a particular month. Given that there were 90 admissions for the 20-25 age group, calculate the number of admissions for all the other age groups. The area of the rectangles of a histogram represents frequency 0 10 20 30 40 50 60 70 80 90 age frequency density 30 27 24 21 18 18 15 12 9 225 6 135 225 90 120 5 3 90 45 30 © T Madas

© T Madas

The histogram below shows the age distribution of accident and emergency admissions in the Colby City Hospital for a particular month. Given that there were 90 admissions for the 20-25 age group, calculate the number of admissions for all the other age groups. The area of the rectangles of a histogram represents frequency 0 10 20 30 40 50 60 70 80 90 age frequency density Squares : 12 : 4 : 6 : 30 : 18 : 16 : Data 90 30 45 225 135 120 90 225 135 225 90 120 90 45 30 © T Madas

© T Madas